Cyclic Quadrilateral Circumradius and Area from Side Lengths

This GeoGebra example demonstrates how a cyclic quadrilateral’s circumradius and area can be determined as functions of its four side lengths, with the results dynamically reflected on the constructed diagram. It centers on the key ideas of cyclic quadrilaterals, circumcircles (circumradius), and angle relations for points on a common circle (using computed interior angles to support the necessary geometric constraints). The construction uses Intersect, Circle, Point, CircleArc, Polygon, InteriorAngles, and Segment to build the circumcircle and the quadrilateral, mark key arcs, and obtain the interior angles that drive the area computation. Named objects such as the circumcenter O, the circle objects c1/c_{2}, vertices A/B/C/D, and auxiliary construction elements (e.g., g, h) are combined with parameter variables (α, β, γ, δ) and output text objects (texto1, R) to present the circumradius and area. Suitable for advanced secondary school and early university geometry instruction, especially for dynamic verification of relationships and formula-based problem solving.